While I'm unaware of these two extremely well known historical incidents having ever been systematically compared before, I think you'll find that the two have some remarkable similarities. In both the case of Joan of Arc, and the Salem Witch Trials, we have adolescent girls manipulating, and being manipulated, by powerful men, to achieve their own objectives, for their own reasons. In both cases, we hear strident cries of "witchcraft". Although Joan of Arc was canonized as a Saint by the Pope during the Babylonian captivity, actually, it's quite clear that she was having a great deal of fun lording it over all the powerful warlords in play, during her period of ascendancy, just like the girls in Salem were loving every second of dominating the community of Salem, and, ultimately, all of New England society, at all levels.

https://salem.lib.virginia.edu/images/mattwitch1.jpg

I think a significant point here is simply the fact that adolescent girls could have such massive, if temporary effect on society, because that's only possible if society is, or is becoming, centralized to a high degree. And, clearly this was the case in both New England and the time of the Witch Trials, and in France when Joan of Arc played her particular role. These young girls tapped into the increasing ability to gather a mass audience and influence it quickly, in their developing societies, to such an extent, that everyone was taken off guard, and surprised, and astonished. And, these facts presage the ultimate revolutions that overturned their respective societies in the coming decades -- both the French, and the Americans, respectively throwing off the yoke of the English, because of centralization of power locally, to repel the English.

Now, the difference here, is that Joan of Arc represented herself as an agent of God, and was burned as a witch, and ultimately became a Saint, while the girls in Salem falsely condemned others as witches, and these Salem girls themselves went on to leave fairly uneventful lives following their brief period of stardom. Joan was a religious girl who had seen the damage the English were doing in her country, who had seen family members killed by them. She convinced herself she was a chosen prophet and savior of her people, probably hormonally driven to some extent. She fought and suffered for her people, achieved some brilliant victories, suffered and survived serious injuries, only to be captured by the English, and done cruelly to death by them. However, she could have been ransomed by the French King, who offered nothing for her. This may have been a mistake. This gave the English the opportunity to discredit the King's instrument in a trial for heresy. In any case, the power games involved here were of a very high order.

https://i.pinimg.com/736x/f2/67/c0/f267c0b69840ffd081706bc78527ced5.jpg

The Salem witch trials more reveal the growing independence and power of the colony of Massachusetts, its government structures, and their ability and facility to influence the people, in response to popular demands. This, of course, grew greater and greater with the coming decades, even if trials for witchcraft were discredited.